SEO- Search Engine optimization
SEM- Search Engine Marketing.
Both are related to Website promotion terms which can be used using various tasks and which is possible to give good Rank as well good traffic for a website.

Search engine marketing: The practice of getting your website visible on the major search engines, such as Google, Yahoo! and MSN. Essentially, SEM is about delivering traffic to your website. Two of the most successful SEM strategies are search engine optimization, and pay-per-click advertising campaigns.

Search engine optimization: A system of methods used to enhance a website's ranking in search engines' natural search results. This includes optimizing the on-page factors, such as using relevant keywords, making sites W3C compliant, and a whole range of other techniques. SEO strategies are constantly evolving as the search engines update their algorithms.

Search Engine Optimization(SEO) can be classified under the larger category referred to as Search Engine Marketing(SEM). Search engine marketing involves all activities that can be used to promote a website, a business or earn a website owner income. SEM involves activities such as paid inclusions,Traditional Ads,Pay per click advertising etc. One of the biggest differences in these two techniques is the SEM is almost guaranteed and takes place immediately but SEO requires more work, monitoring and patience to yield results. SEM is more expensive because it is a fast and reliable way of promoting a website.*

SEO which refers to everything you do on your website to make it extra users as well as friendly.
SEM stands for search engine marketing, it works as an umbrella which refers to something you do to get your page ranked high on the search engine.